Apparent Contradiction : In the above couplet there appears to be a contradiction. How can dvapara, come after the the third yuga is over? We know that the sequence of yugas is Kruta, Tretha, Dvapara and Kali. While this Source explains this by speaking of an “overlapping” of yugas, my reasoning is given below.

Resolution :

Dharma walks on four feet in Kruta/Satya, on three in Tretha, on two in Dwapara and on one in Kali. So the Yuga that was over was the one in which Dharma walked on 3 feet. The yuga that was approaching was the one in which Dharma walks on 2 feet.

Therefore, Vyasa was born in the Tretha Yuga as the Dvapara Yuga approached and lived to see the early part of Kaliyuga. So he was a chiranjeeva, a long lived one.

Source : 1.3.21 : States that Vyasa, son of Satyavati and Parasara was the 17th Avatara

Apparent Contradiction : How can Vyasa be prior to Sri Rama and be born in the sandhi of the tretha and the dwapara yugas? Using the correct translation of 1.4.14, there is no contradiction. Vyasa was born in the Tretha Yuga prior to Sri Rama.

While it is generally worked out that Sri Rama was of the Tretha Yuga, upto this point I have not found direct reference in the Valmiki Ramayanam or in the Vyasa Bhagavatham to support this assumption. I am still looking.